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Constrained derivative-free optimization on thin domains

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  • J. Martínez
  • F. Sobral

Abstract

Many derivative-free methods for constrained problems are not efficient for minimizing functions on “thin” domains. Other algorithms, like those based on Augmented Lagrangians, deal with thin constraints using penalty-like strategies. When the constraints are computationally inexpensive but highly nonlinear, these methods spend many potentially expensive objective function evaluations motivated by the difficulties in improving feasibility. An algorithm that handles this case efficiently is proposed in this paper. The main iteration is split into two steps: restoration and minimization. In the restoration step, the aim is to decrease infeasibility without evaluating the objective function. In the minimization step, the objective function f is minimized on a relaxed feasible set. A global minimization result will be proved and computational experiments showing the advantages of this approach will be presented. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • J. Martínez & F. Sobral, 2013. "Constrained derivative-free optimization on thin domains," Journal of Global Optimization, Springer, vol. 56(3), pages 1217-1232, July.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:3:p:1217-1232
    DOI: 10.1007/s10898-012-9944-x
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    References listed on IDEAS

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    1. Charles Audet & J. Dennis & Sébastien Digabel, 2010. "Globalization strategies for Mesh Adaptive Direct Search," Computational Optimization and Applications, Springer, vol. 46(2), pages 193-215, June.
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    Cited by:

    1. Boukouvala, Fani & Misener, Ruth & Floudas, Christodoulos A., 2016. "Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO," European Journal of Operational Research, Elsevier, vol. 252(3), pages 701-727.

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